Integral solutions for transient fluid flow through a porous medium with pressure-dependent permeability

Abstract

This paper presents an integral method for analyzing transient fluid flow through a porous medium , which has pressure-dependent permeability. Approximate analytical solutions have been obtained for one-dimensional linear and radial flow by an integral-solution technique, in which the density of the fluid, and the porosity and permeability of the formation, are treated as arbitrary functions of pressure. The integral solutions have been checked by comparison with exact solutions for constant-permeability cases and with numerical simulation results for general non-linear flow problems, and good agreement has been obtained for both cases. In the study of transient flow of fluids through porous media, intrinsic or absolute permeability of the formation has often been treated as a constant in order to avoid solving a non-linear problem. The present work shows that the assumption of a pressure-independent permeability may introduce significant errors for flow in certain pressure sensitive media. Application of the integral solutions to slightly compressible fluid flow in a horizontal fracture set is illustrated. The calculations show that neglect of changes in fracture permeability leads to large errors under the condition of high injection pressure .